Beard Balm and Beard Oil are two very similar products that can achieve similar results, or different results. A beard oil is a conditioning product that you apply and leave in to soften a beard, help it smell great, and minimize dry skin and flakiness.
A beard balm can be a conditioning product like a beard oil, or it could also be a sculpting product which will help tame the beard and give it shape. With a conditioning balm you'l get slightly more control than a beard oil because it's a butter based product. Butters are like shea butter, cocoa butter, or mango butter.
A sculpting beard balm will most likely also include waxes and lean towards the harder butters to help keep the beard in it's place. It's important to buy a product that is providing the type of results you are looking for. Look in the back to see if beeswax (or other waxes) are part of the ingredient list.
I'd recommend staying away from products that list water as their primary ingredient. Frequently they'll use silicones to give the feeling of a balm, without using the premium ingredients. That being said, every product is different and not all water based products are "bad." It's important to do your own research on ingredients and be aware of what you are putting on your skin and beard.